Browsing by Author "Mahmoudi, Mohammad Reza"

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A Bayesian Approach to Heavy-Tailed Finite Mixture Autoregressive Models
(2020) Baleanu, Dumitru; Maleki, Mohsen; Baleanu, Dumitru; Nguye, Vu-Thanh; Pho, Kim-Hung; 56389
In this paper, a Bayesian analysis of finite mixture autoregressive (MAR) models based on the assumption of scale mixtures of skew-normal (SMSN) innovations (called SMSN-MAR) is considered. This model is not simultaneously sensitive to outliers, as the celebrated SMSN distributions, because the proposed MAR model covers the lightly/heavily-tailed symmetric and asymmetric innovations. This model allows us to have robust inferences on some non-linear time series with skewness and heavy tails. Classical inferences about the mixture models have some problematic issues that can be solved using Bayesian approaches. The stochastic representation of the SMSN family allows us to develop a Bayesian analysis considering the informative prior distributions in the proposed model. Some simulations and real data are also presented to illustrate the usefulness of the proposed models.
A Novel Method to Detect Almost Cyclostationary Structure
(Elsevier B.V., 2020) Baleanu, Dumitru; Baleanu, Dumitru; Anh Tuan, B.; Pho, K. H.; 56389
This paper is devoted to establish a computational approach to investigate that a discrete-time almost cyclostationary model is a suitable choice to fit on an observed dataset. The main idea is estimating the support of spectra and applying multiple testing. The simulated and real datasets are applied to study the performance of the introduced approach. The results confirm that the presented method acts efficiently in view of power study.
Chebyshev Cardinal Functions for A New Class of Nonlinear Optimal Control Problems With Dynamical Systems of Weakly Singular Variable-Order Fractional Integral Equations
(Sage Publications INC, 2020) Baleanu, Dumitru; Mahmoudi, Mohammad Reza; Avazzadeh, Zakieh; Baleanu, Dumitru; 56389
The main objectives of this study are to introduce a new class of optimal control problems governed by a dynamical system of weakly singular variable-order fractional integral equations and to establish a computational method by utilizing the Chebyshev cardinal functions for their numerical solutions. In this way, a new operational matrix of variable-order fractional integration is generated for the Chebyshev cardinal functions. In the established method, first the control and state variables are approximated by the introduced basis functions. Then, the interpolation property of these basis functions together with their mentioned operational matrix is applied to derive an algebraic equation instead of the objective function and an algebraic system of equations instead of the dynamical system. Eventually, the constrained extrema technique is applied by adjoining the constraints generated from the dynamical system to the objective function using a set of Lagrange multipliers. The accuracy of the established approach is examined through several test problems. The obtained results confirm the high accuracy of the presented method.
Factor analysis approach to classify COVID-19 datasets in several regions
(2021) Baleanu, Dumitru; Baleanu, Dumitru; Band, Shahab S.; Mosavi, Amir; 56389
The aim of this research is to investigate the relationships between the counts of cases with Covid-19 and the deaths due to it in seven countries that are severely affected from this pandemic disease. First, the Pearson's correlation is used to determine the relationships among these countries. Then, the factor analysis is applied to categorize these countries based on their relationships. © 2021 The Authors
Fuzzy clustering method to compare the spread rate of Covid-19 in the high risks countries
(2020) Baleanu, Dumitru; Baleanu, Dumitru; Mansor, Zulkefli; Tuan, Bui Anh; Pho, Kim-Hung; 56389
The numbers of confirmed cases of new coronavirus (Covid-19) are increased daily in different countries. To determine the policies and plans, the study of the relations between the distributions of the spread of this virus in other countries is critical. In this work, the distributions of the spread of Covid-19 in Unites States America, Spain, Italy, Germany, United Kingdom, France, and Iran were compared and clustered using fuzzy clustering technique. At first, the time series of Covid-19 datasets in selected countries were considered. Then, the relation between spread of Covid-19 and population's size was studied using Pearson correlation. The effect of the population's size was eliminated by rescaling the Covid-19 datasets based on the population's size of USA. Finally, the rescaled Covid-19 datasets of the countries were clustered using fuzzy clustering. The results of Pearson correlation indicated that there were positive and significant between total confirmed cases, total dead cases and population's size of the countries. The clustering results indicated that the distribution of spreading in Spain and Italy was approximately similar and differed from other countries. © 2020 Elsevier Ltd
Fuzzy clustering to classify several time series models with fractional Brownian motion errors
(2021) Baleanu, Dumitru; Baleanu, Dumitru; Qasem, Sultan Noman; Mosavi, Amirhosein; S. Band, Shahab; 56389
In real world problems, scientists aim to classify and cluster several time series processes that can be used for a dataset. In this research, for the first time, based on fuzzy clustering method, an approach is applied to classify and cluster several time series models with fractional Brownian motion errors as candidates to fit on a dataset. The ability of the introduced technique is studied using simulation and real world example. © 2020 THE AUTHORS
On Comparing and Classifying Several Independent Linear and Non-Linear Regression Models with Symmetric Errors
(MDPI, 2019) Baleanu, Dumitru; Mahmoudi, Mohammad Reza; Baleanu, Dumitru; Maleki, Mohsen; 56389
In many real world problems, science fields such as biology, computer science, data mining, electrical and mechanical engineering, and signal processing, researchers aim to compare and classify several regression models. In this paper, a computational approach, based on the non-parametric methods, is used to investigate the similarities, and to classify several linear and non-linear regression models with symmetric errors. The ability of each given approach is then evaluated using simulated and real world practical datasets.
On comparing and clustering the spectral densities of several almost cyclostationary processes
(2020) Baleanu, Dumitru; Maleki, Mohsen; Borodin, Kirill; Pho, Kim-Hung; Baleanu, Dumitru; 56389
In time series analysis, comparing spectral densities of several processes with almost peri-odic spectra is an interested problem. The contribution of this work is to give a technique to com-pare and to cluster the spectral densities of some independent almost periodically correlated (cyclostationary) processes. This approach is based on the limiting distribution for the periodogram and the discrete Fourier transform. The real world examples and simulation results indicate that the approach well acts. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/ 4.0/).
The Properties of a Decile-Based Statistic to Measure Symmetry and Asymmetry
(2020) Baleanu, Dumitru; Nasirzadeh, Roya; Baleanu, Dumitru; Pho, Kim-Hun; 56389
This paper studies a simple skewness measure to detect symmetry and asymmetry in samples. The statistic can be obviously applied with only three short central tendencies; i.e., the first and ninth deciles, and the median. The strength of the statistic to find symmetry and asymmetry is studied by employing numerous Monte Carlo simulations and is compared with some alternative measures by applying some simulation studies. The results show that the performance of this statistic is generally good in the simulation.